Bloody Palace

The Bloody Palace is a game mode available in all Devil May Cry games except for the first. It is a single-elimination tournament that pits the player character against many groups of enemies and bosses, each on a lower floor, until they reach the end of the Palace.

Devil May Cry 2
In Devil May Cry 2, there are 9999 floors, culminating a fight against nearly every boss in the game. Unlike later versions, there is no reward for completing the palace, and you will restart at the first floor after beating the last (It means that this additional mode was intended for the player to master his/her skills and abilities as well as gaining a large sum of Red Orbs). The enemy groupings are semi-random for each run through the palace.

Devil May Cry 3
In Devil May Cry 3: Special Edition, but not in the original release, the Bloody Palace has 9999 floors, and completing it with a character allows them to obtain their Super costumes even without completing the Very Hard or Dante/Vergil Must Die game mode. After you passed one level, you were given 3 portals to choose; the water portal lets you advance one level, the lightning portal lets you advance 10 levels, and the fire portal lets you advance 100 levels.

Devil May Cry 4
In Devil May Cry 4, there are only 101 floors, with bosses fought on every twenty floors, culminating with Dante on the 101st floor (but if playing as Dante himself until the last floor, an all-black Dante will be fought instead, considered by some to be the doppelganger's appearence in this game). Unlike other incarnations of the palace, the enemy groupings are set, and the player can only travel one floor at a time. Furthermore, the player has a finite amount of time in the palace, though time bonuses can be obtained for defeating all the enemies, defeating them with higher stylish ranks, or clearing an entire floor, with a bonus for clearing it without taking any damage, while defeating bosses gives the highest additional time.

For Devil May Cry 4, the Bloody Palace can provide some interesting fights not available throughout the campaign, especially when you are playing as Dante. Aside from the new black Dante boss fight, Bloody Palace allows the player to fight Angelo Agnus (in his chamber), Bael, or Angelo Credo. Furthermore, it is only in Bloody Palace mode wherein the player can see the complete in-game animation of Angelo Credo's death.

Background
For Devil May Cry 4, there are several achievements regarding the Bloody Palace, nine of which are actually based from the Divine Comedy. These start at the First Circle and work their way up to the Ninth Circle. In the Divine Comedy, these are collectively known as the Circles of Hell wherein souls who suffered from a specific sin are being gathered at a specified circle, and are being given at the same punishment.